Problem 3. Consider the following LP. max X1,X2,X3,X4 3x1 + x2 s.t. 2x1 + x2 + x3 = 6 -X1 + x2 + X4 = 3 X1, X2, X3, X4 2 0 1) Use the Simplex method to solve this LP. You can start with any basic...

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Extracted text: Problem 3. Consider the following LP. max X1,X2,X3,X4 3x1 + x2 s.t. 2x1 + x2 + x3 = 6 -X1 + x2 + X4 = 3 X1, X2, X3, X4 2 0 1) Use the Simplex method to solve this LP. You can start with any basic feasible solution (BFS). Explicitly show the BFS that you apply in the beginning of your solution. 2) Suppose the coefficient of x, in the first constraint will be changed (currently, it is 2). What is the range of the coefficient such that the current optimal basis can be kept? [Hint for part 2): run the simplex method including the change of the coefficient, and apply the optimality condition(s).]